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A topology optimization method based on element independent nodal density

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Abstract

A methodology for topology optimization based on element independent nodal density (EIND) is developed. Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function. The influence of the diameter of interpolation is discussed which shows good robustness. The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint. The rational approximation for material properties (RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions. Solutions are shown to meet stability, mesh dependence or non-checkerboard patterns of topology optimization without additional constraints. Finally, the computational efficiency is greatly improved by multithread parallel computing with OpenMP.

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Central South University, Changsha, 410083, China

    Ji-jun Yi  (易继军) & Tao Zeng  (曾韬)

  2. School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha, 410004, China

    Ji-jun Yi  (易继军) & Jian-hua Rong  (荣见华)

  3. Hunan Technical College of Water Resources and Hydro Power, Changsha, 410131, China

    Yan-mei Li  (李艳梅)

Authors
  1. Ji-jun Yi  (易继军)
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  2. Tao Zeng  (曾韬)
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  3. Jian-hua Rong  (荣见华)
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  4. Yan-mei Li  (李艳梅)
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Corresponding author

Correspondence to Ji-jun Yi  (易继军).

Additional information

Foundation item: Projects(11372055, 11302033) supported by the National Natural Science Foundation of China; Project supported by the Huxiang Scholar Foundation from Changsha University of Science and Technology, China; Project(2012KFJJ02) supported by the Key Labortory of Lightweight and Reliability Technology for Engineering Velicle, Education Department of Hunan Province, China

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Yi, Jj., Zeng, T., Rong, Jh. et al. A topology optimization method based on element independent nodal density. J. Cent. South Univ. 21, 558–566 (2014). https://doi.org/10.1007/s11771-014-1974-8

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  • DOI: https://doi.org/10.1007/s11771-014-1974-8

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